Al Qaeda in the Arabian Peninsula claimed responsibility on Monday for the unsuccessful Christmas Day effort to bring down a jet over Detroit, while the Obama administration rushed to deal with the political fallout from the attack.

President Obama issued his first statement on the attack, telling Americans that his government was doing everything in its power to keep them safe. Hours earlier, the homeland security secretary backed away from her comments Sunday that “the system worked.”

Al Qaeda in the Arabian Peninsula, a group that claims loyalty to Osama bin Laden, said in posts left on jihadist Web forums that the plot against Northwest Airlines Flight 253 was launched in response to recent “American aggression” in Yemen, which has been the site of recent U.S. predator drone attacks.

The group boasted that Umar Farouk Abdulmutallab managed to avoid detection by screening machines when he boarded a plane in Amsterdam bound for Detroit with “a technologically advanced [explosive] device” hidden in his underpants.

Mr. Abdulmutallab, 23, is in custody and is scheduled to appear in court Jan. 8 to answer charges that he tried to destroy the plane and kill the nearly 300 people on board.

During the jet’s final approach to Detroit, Mr. Abdulmutallab attempted to set off the device, U.S. authorities say, but succeeded only in causing a small fire in the cabin and burning himself before other passengers subdued him.

Al Qaeda in the Arabian Peninsula described the device’s failure to explode as “technical difficulties.”

The group also called on Muslims to “kill every crusader who works at an embassy or elsewhere, and to declare an all-encompassing war on every crusader in the Peninsula of Muhammad, prayers and peace be upon him.”

The statement called on every “soldier who works for the crusader armies and the agent governments to repent unto God and emulate the example of the heroic mujahid brother, Nidal Hasan.”

Maj. Nidal Malik Hasan is the Army officer charged with killing 13 people during a shooting spree in November at Fort Hood, Texas.

A U.S. counterterrorism official called al Qaeda in the Arabian Peninsula’s claim “certainly credible” and “in keeping with the group’s growing desire to strike Western interests beyond the Arabian Peninsula.”

Also, a U.S. intelligence official who is familiar with the FBI’s interrogation of Mr. Abdulmutallab said that during questioning, the suspect made similar claims to those of al Qaeda in the Arabian Peninsula.

Mr. Abdulmutallab “was already in jihad training, but they sped it up as a response to the Predator attacks,” the official said, based on the suspect’s words.

While the intelligence official cautioned that Mr. Abdulmutallab may simply have been talking tough, he told his interrogators that “this is just the beginning.”

“I beat your security and you can’t stop us,” the intelligence official cited Mr. Abdulmutallab as telling the FBI.

The intelligence official said Dutch and U.S. law-enforcement authorities are taking seriously and investigating a report that Mr. Abdulmutallab was allowed on the plane without a passport.

Kurt Haskell, a passenger on the flight, told the Detroit News that he saw Mr. Abdulmutallab try to board a flight without a passport.

Mr. Haskell, who was returning from an African safari with his wife, also told the newspaper that he saw a well-dressed man ask the ticket agents whether Mr. Abdulmutallab could get on the flight without a passport, apparently insinuating that he was a Sudanese refugee without proper documentation.

“We’re also very interested in the gentleman who drove them to the airport. … The Dutch are doing an investigation and they have promised to share with us the results,” the intelligence official told The Times.

Yemen’s Ministry of Foreign Affairs said Monday that Mr. Abdulmutallab was in that country from early August to early December after he obtained a visa to study Arabic at a school where he had previously studied.

The Yemen government said that there was nothing suspicious about Mr. Abdulmutallab’s visit and that he had a valid visa to the U.S. and other countries.

Yemeni security agencies are working to identify any other people involved in the apparent plot, and the government said the results of that probe will be shared with U.S. authorities.

Making his first public statement since the unsuccessful attack, Mr. Obama expressed concerns about Mr. Abdulmutallab’s ability to board the plane and ordered a review of the case.

Mr. Obama is particularly eager to know why a person whose name was on a U.S. terrorist watch list was permitted to board a flight to the United States.

In a statement released Monday, Mr. Abdulmutallab’s relatives said they reported concerns to Nigerian and some foreign security agencies more than a month ago, after the young man stopped communicating with his family. Mr. Abdulmutallab ended up on the watch list as a result.

The information from Mr. Abdulmutallab’s family triggered a Nov. 20 State Department cable from Lagos, Nigeria, to all U.S. diplomatic missions and department headquarters in Washington. It also was shared with the interagency National Counterterrorism Center, said State Department spokesman Ian Kelly, the Associated Press reported.

The NCTC, which has responsibility if any visas are to be pulled over terrorism concerns, then reviewed the information and found it was “insufficient to determine whether his visa should be revoked,” Mr. Kelly said.

The president also said Monday that he wants the review to determine how Mr.Abdulmutallab was able to pass through security and smuggle explosives onto the jet.

“We do not yet have all the answers about this latest attempt, but those who would slaughter innocent men, women and children must know that the United States will do more than simply strengthen our defenses,” said Mr. Obama, who is spending the holidays in Hawaii. “We will continue to use every element of our national power to disrupt, to dismantle and defeat the violent extremists who threaten us.”

On Capitol Hill, Sen. Joe Lieberman, Connecticut independent and chairman of the Homeland Security and Governmental Affairs Committee, said he will call a January hearing to investigate the handling of U.S. terrorist suspect lists and why body-imaging scanners are not used on more passengers.

Also on Monday, Homeland Security Secretary Janet Napolitano said her statements a day earlier that “the system worked” were taken out of context.

“The whole process of making sure that we respond properly, correctly and effectively went very smoothly,” Ms. Napolitano also said Sunday on CNN’s “State of the Union.”

Ms. Napolitano said Monday that she had been referring to the government’s success in contacting and notifying other airports and aircraft immediately upon learning of the plot on Christmas Day.

She conceded during television interviews with several networks Monday that the system failed badly in preventing a potential devastating attack.

“Our system did not work in this instance,” she said on NBC’s “Today” show. “No one is happy or satisfied with that. An extensive review is under way.”

Domestic and international travelers described widely differing levels of security to reporters at U.S. airports Monday.

Some airline officials told the Associated Press and Reuters that the in-flight restrictions had been eased, giving captains discretion on matters such as whether passengers can have blankets or other items on their laps and can move about the aircraft in the last hour of the flight. But a Transportation Security Administration spokeswoman declined to confirm that.